Calculation of permeability

Figure 17.23. Calculation of permeability fractal dimension for mixtures of the high melting fraction of milkfat and sunflower oil fat.

L.C., Drake, H.L., Ritter. 1945. Macropore-Size Distributions in Some Typical and the Calculation of Permeability Therefrom, Ind. and Eng. Chem. Analytical Edition, vol. 17, 787 pages. 

Considerations in the Calculation of Permeability from PAMPA Data... 

The calculations of permeability (P) and diffusion (D) coefficients from the continuous flow method are illustrated in Fig. 14.11. P and D are calculated as follows ... 

Note that the thickness of the polymer sample is required for the calculation of permeabilities (see equation 1). As the temperature is increased, the polymer volume, and therefore the thickness, increases. We have not measured volume expansions over this temperature range. Therefore, the data in Figure 4 have not been corrected for thickness variations. Structurally similar polyimides have been shown to increase in thickness by approximately 5% over this temperature range (25). 

Dielectric properties of other curing epoxy resin systems, that is, DGEBA (DER 332) and DDS, Jeffamine D-230, or mPDA, at a frequency of 2.45 GHz in the temperature range of 20-100 °C can also be found in the literature together with the theoretical model for calculation of permeability (e ) and the loss factor (e") during curing epoxy systems under micro-wave irradiation. ... 

Deli et al. (2005) presented permeability data from various in vitro BBB models by measuring transendothe-lial electrical resistance (TEER) and by calculation of permeability coefficients for paracellular or transendothelial tracers. These authors summarized the results of primary cultures of cerebral microvascular endothelial cells or immortalized cell lines from bovine, human, porcine, and rodent origin. This also described the effect of coculture with astroglia, neurons, mesenchymal cells, blood cells, and conditioned media, as well as the physiological influence of serum components, hormones, growth factors, lipids, and lipoproteins on the BBB fimction. 

Plasticization and Other Time Effects Most data from the literature, including those presented above are taken from experiments where one gas at a time is tested, with Ot calculated as a ratio of the two permeabihties. If either gas permeates because of a high-sorption coefficient rather than a high diffusivity, there may be an increase in the permeabihty of all gases in contact with the membrane. Thus, the Ot actually found in a real separation may be much lower than that calculated by the simple ratio of permeabilities. The data in the hterature do not rehably include the plasticization effect. If present, it results in the sometimes slow relaxation of polymer structure giving a rise in permeabihty and a dramatic dechne in selectivity. 

However, before proceeding with the description of simulation data, we would like to comment the theoretical background. Similarly to the previous example, in order to obtain the pair correlation function of matrix spheres we solve the common Ornstein-Zernike equation complemented by the PY closure. Next, we would like to consider the adsorption of a hard sphere fluid in a microporous environment provided by a disordered matrix of permeable species. The fluid to be adsorbed is considered at density pj = pj-Of. The equilibrium between an adsorbed fluid and its bulk counterpart (i.e., in the absence of the matrix) occurs at constant chemical potential. However, in the theoretical procedure we need to choose the value for the fluid density first, and calculate the chemical potential afterwards. The ROZ equations, (22) and (23), are applied to decribe the fluid-matrix and fluid-fluid correlations. These correlations are considered by using the PY closure, such that the ROZ equations take the Madden-Glandt form as in the previous example. The structural properties in terms of the pair correlation functions (the fluid-matrix function is of special interest for models with permeabihty) cannot represent the only issue to investigate. Moreover, to perform comparisons of the structure under different conditions we need to calculate the adsorption isotherms pf jSpf). The chemical potential of a... 

The sizes and concentration of the free-volume cells in a polyimide film can be measured by PALS. The positrons injected into polymeric material combine with electrons to form positroniums. The lifetime (nanoseconds) of the trapped positronium in the film is related to the free-volume radius (few angstroms) and the free-volume fraction in the polyimide can be calculated.136 This technique allows a calculation of the dielectric constant in good agreement with the experimental value.137 An interesting correlation was found between the lifetime of the positronium and the diffusion coefficient of gas in polyimide.138,139 High permeabilities are associated with high intensities and long lifetime for positron annihilation. 

In PAMPA measurements each well is usually a one-point-in-time (single-timepoint) sample. By contrast, in the conventional multitimepoint Caco-2 assay, the acceptor solution is frequently replaced with fresh buffer solution so that the solution in contact with the membrane contains no more than a few percent of the total sample concentration at any time. This condition can be called a physically maintained sink. Under pseudo-steady state (when a practically linear solute concentration gradient is established in the membrane phase see Chapter 2), lipophilic molecules will distribute into the cell monolayer in accordance with the effective membrane-buffer partition coefficient, even when the acceptor solution contains nearly zero sample concentration (due to the physical sink). If the physical sink is maintained indefinitely, then eventually, all of the sample will be depleted from both the donor and membrane compartments, as the flux approaches zero (Chapter 2). In conventional Caco-2 data analysis, a very simple equation [Eq. (7.10) or (7.11)] is used to calculate the permeability coefficient. But when combinatorial (i.e., lipophilic) compounds are screened, this equation is often invalid, since a considerable portion of the molecules partitions into the membrane phase during the multitimepoint measurements. 

The airflow equations presented above are based on the assumption that the soil is a spatially homogeneous porous medium with constant intrinsic permeability. However, in most sites, the vadose zone is heterogeneous. For this reason, design calculations are rarely based on previous hydraulic conductivity measurements. One of the objectives of preliminary field testing is to collect data for the reliable estimation of permeability in the contaminated zone. The field tests include measurements of air flow rates at the extraction well, which are combined with the vacuum monitoring data at several distances to obtain a more accurate estimation of air permeability at the particular site. 

Transmissivity is simply the coefficient of permeability, or the hydraulic conductivity (k), within the plane of the material multiplied by the thickness (T) of the material. Because the compressibility of some polymeric materials is very high, the thickness of the material needs to be taken into account. Darcy s law, expressed by the equation Q = kiA, is used to calculate the rate of flow, with transmissivity equal to kT and i equal to the hydraulic gradient (see Figure 26.22) ... 

JH Kou, D Fleisher, GL Amidon. Calculation of the aqueous diffusion layer resistance for absorption in a tube Application to intestinal membrane permeability determination. Pharm Res 8 298-305, 1991. 

We measure the permeation rate of liquids through bottles by filling them with the liquid of interest and placing them in a controlled atmosphere chamber. At intervals we remove the bottles, weigh them and return them to the chamber. We repeat this procedure over a period of days, or even weeks, until their rate of weight loss reaches a steady value. We calculate the permeability factor from Eq. 8.10. 

Similarly, in 3D-radial geometries of interest for petroleum engineers, an equivalent wellbore radius re is defined. The near-wellbore region, including radially distributed wormholes from rw up to re, is infinitely permeable and therefore becomes a mere radial extension of the wellbore itself. Equation 2 can be used to calculate the pseudodecrease of the skin when an undamaged primary porosity formation of permeability k0 includes wormholes as described hereabove ... 

In addition, the calculation of many different ID, 2D and 3D descriptors is possible using a range of commercially available software packages, such as Sybyl, Cerius2, Tsar, Molconn-Z and Hybot. Several new descriptor sets are based on quantification of 3D molecular surface properties, and these have been explored for the prediction of, e.g., Caco-2 permeability and oral absorption. It is pointed out here that a number of these new descriptors are strongly correlated to the more traditional physico-chemical properties. 

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